Analytic and numerical modeling of the transient dynamics of a microcantilever sensor

Microcantilevers have recently emerged as sensor components that hold the promise for robust detection of biological, chemical, and other security-related threats. Consequently, there has been a growing need to develop accurate and sophisticated methods for predicting a microcantilever's transient response to an arbitrary spatio-temporal load. To model the spatio-temporal dynamics of the microcantilever, the non-homogeneous beam equation, a fourth-order partial differential equation, is used. This Letter presents an innovative analytical solution of this equation, including damping and spatio-temporal shifts. This solution is compared to a numerical, stable finite-differences implementation. Excellent agreement is shown for two examples of forcing by shifted spatio-temporal loads, including a finite-width Gaussian pulse. The computer code implementation is also discussed. (C) 2007 Elsevier B.V. All rights reserved.